arXiv:1912.05795 · Physical review. B./Physical review. B

High-resolution spectroscopy of individual erbium ions in strong magnetic fields

Gabriele G. de Boo, Chunming Yin, Miloš Rančić, Brett C. Johnson, Jeffrey Colin McCallum, Matthew J. Sellars, Sven M. J. Rogge

Published Oct 23, 2020• 12 citations

arXiv HTML PDF

Abstract

In this paper, we use electrically detected optical excitation spectroscopy of individual erbium ions in silicon to determine their optical and paramagnetic properties simultaneously. We demonstrate that this high spectral resolution technique can be exploited to observe interactions typically unresolvable in silicon using conventional spectroscopy techniques due to inhomogeneous broadening. In particular, we resolve the Zeeman splitting of the $^{4}\mathrm{I}_{15/2}$ ground and $^{4}\mathrm{I}_{13/2}$ excited state separately, and in strong magnetic fields, we observe the anticrossings between Zeeman components of different crystal-field levels. We discuss the use of this electronic detection technique to aid in the identification of the symmetry and structure of erbium sites in silicon.

DOI: 10.1103/physrevb.102.155309

Related papers

Single site optical spectroscopy of coupled Er 3+ ion pairs in silicon

Guangchong Hu, Rose L. Ahlefeldt, Gabriele G. de Boo +6 more

arXiv:2108.07442Quantum Science and TechnologyFeb 18, 20228 citations

High Resolution Spectroscopy of Erbium Doped Solids

Miloš Rančić

Jan 1, 20173 citations

Prediction of optical polarization and high-field hyperfine structure via a parametrized crystal-field model for low-symmetry centers in Er3+ -doped Y2SiO5

Nicholas Jobbitt, J.‐P. R. Wells, Michael F. Reid +3 more

arXiv:2206.09080Physical review. B./Physical review. BOct 13, 202115 citations

Hyperfine interaction of Er 3 + ions in Y 2 Si O 5 : An electron paramagnetic resonance spectroscopy study

O. Guillot-Noël, Philippe Goldner, Y. Le Du +3 more

Physical Review BDec 11, 200681 citations

High-resolution magneto-optical spectroscopy of LiYF47:Er3+167,Er3+166 and analysis of hyperfine structure of ultranarrow optical transitions

K. I. Gerasimov, Mansur M. Minnegaliev, Malkin Boris Zalmanovich +2 more

Physical review. B./Physical review. BAug 29, 201629 citations

Magnetic g tensors for the I 15 ∕ 2 4 and I 13 ∕ 2 4 states of Er 3 + : Y 2 Si O 5

Yongchen Sun, Thomas Böttger, Charles W. Thiel +1 more

Physical Review BFeb 29, 200891 citations

arXiv:1912.05795 · Physical review. B./Physical review. B

High-resolution spectroscopy of individual erbium ions in strong magnetic fields

Gabriele G. de Boo, Chunming Yin, Miloš Rančić, Brett C. Johnson, Jeffrey Colin McCallum, Matthew J. Sellars, Sven M. J. Rogge

Published Oct 23, 2020• 12 citations

arXiv HTML PDF

Abstract

^{4}\mathrm{I}_{15/2}

ground and

^{4}\mathrm{I}_{13/2}

excited state separately, and in strong magnetic fields, we observe the anticrossings between Zeeman components of different crystal-field levels. We discuss the use of this electronic detection technique to aid in the identification of the symmetry and structure of erbium sites in silicon.

DOI: 10.1103/physrevb.102.155309

Related papers

Single site optical spectroscopy of coupled Er 3+ ion pairs in silicon

Guangchong Hu, Rose L. Ahlefeldt, Gabriele G. de Boo +6 more

Abstract Individual optical emitters coupled via coherent interactions are attractive qubits for quantum communications applications. Here, we present the first study of single pairs of interacting rare earth ions and determine the interactions between ions in the pair with high resolution. We identify two examples of Er 3+ pair sites in Er implanted Si and characterise the interactions using optical Zeeman spectroscopy. We identify one pair as two Er 3+ ions in sites of at least C 2 symmetry coupled via a large, 200 GHz, Ising-like spin interaction in both optical ground and excited states. The high measurement resolution allows non-Ising contributions to the interaction of < 1 % to be observed, attributed to site distortion. By bringing two optical transitions into resonance with a magnetic field, we observe a 0.8 GHz optical interaction of unusual magnetic-dipole/electric-dipole character with strong polarization selection rules. We discuss the use of this type of strongly coupled, field-tunable rare earth pair system for quantum processing.Abstract Individual optical emitters coupled via coherent interactions are attractive qubits for quantum communications applications. Here, we present the first study of single pairs of interacting rare earth ions and determine the interactions between ions in the pair with high resolution. We identify two examples of Er 3+ pair sites in Er implanted Si and characterise the interactions using optical Zeeman spectroscopy. We identify one pair as two Er 3+ ions in sites of at least C 2 symmetry coupled via a large, 200 GHz, Ising-like spin interaction in both optical ground and excited states. The high measurement resolution allows non-Ising contributions to the interaction of < 1 % to be observed, attributed to site distortion. By bringing two optical transitions into resonance with a magnetic field, we observe a 0.8 GHz optical interaction of unusual magnetic-dipole/electric-dipole character with strong polarization selection rules. We discuss the use of this type of strongly coupled, field-tunable rare earth pair system for quantum processing.

arXiv:2108.07442Quantum Science and TechnologyFeb 18, 20228 citations

High Resolution Spectroscopy of Erbium Doped Solids

Miloš Rančić

This thesis investigates the potential of Er:YSO and Er:Si for quantum communication and computation applications. Erbium uniquely possess optical transitions in the 1.5 um region, making it suitable for both fibre telecommunication and silicon photonics. The properties of the ${I}_{15/2}\leftrightarrow{I}_{13/2}$ optical transition in Er:YSO have already been extensively studied. Over two decades ago, improvements in $Er^{3+}$ dephasing time at 1.5 um were achieved by applying a 5T field along the D1 axis. More recently, a record 4.4 ms coherence time on the same optical transition was achieved using a 7T field. These investigations, among others, illustrate that large Er electron spins become thermally polarised with sufficient magnetic field. However, no long lived and coherent spin transitions associated with the Er ions had previously been identified, and such transitions are necessary for on-demand quantum state storage. To address this requirement, the optical and hyperfine transition properties of 167-Er:YSO were investigated in large magnetic fields. In a field of 7T, spectral hole lifetimes of 1 minute and hyperfine population lifetimes of 12 minutes were observed. These measurements illustrate the effect of spin-lattice relaxation in this system, and how it can be mitigated. Efficient spin-polarisation of the entire 167-Er hyperfine ensemble is also demonstrated. This is the first such demonstration in rare earth systems, and a key requirement for broadband optical storage. Moreover, a 1.3 second coherence time was recorded for an 167-Er:YSO hyperfine transition at 7T and 1.4 K. This is an improvement of several orders-of-magnitude over previous coherence measurements on spin-transitions in Er doped solids. This is also sufficient for maximal entanglement rates in quantum repeater networks that span distances of 1000 km or greater. With an optical transition at 1.5 um, Er is also an ideal candidate to connect silicon based quantum computers to the future quantum Internet. In particular, single Er:Si ions could be used to develop an optical-spin bus between P:Si qubits and fibre based quantum networks. Presented here is the first spectroscopic investigation of single Er:Si ions. This required a novel opto-electronic approach to single ion detection, where the Er ions are implanted into a nanometre scale fin-shaped Field Effect Transistor. With this approach it was possible to develop high resolution optical spectra, where both the electronic and hyperfine levels of individual Er ions were resolved. Long optical and spin coherence times are also important requirements for an optical-spin bus. To address the first requirement, an investigation of the optical lineshape was undertaken. Here it was determined that sources of Stark noise external to the transistor channel contribute a significant amount to optical homogeneous linewidth. However, the dominant noise contribution was determined to be short-range (from within the 30 nm wide channel) and the total homogeneous linewidth was measured to be 50 MHz. The site structure of an individual Er:Si ion was then analysed, using magnetic field rotation patterns and optical transitions between multiple crystal field levels. This site was determined to have approximately axial ( $C_{3}$ ) symmetry. The purpose of this study was to determine a magnetic field regime in which the Er electrons spin can be polarised, which is necessary for realising of long hyperfine lifetimes and coherence times.This thesis investigates the potential of Er:YSO and Er:Si for quantum communication and computation applications. Erbium uniquely possess optical transitions in the 1.5 um region, making it suitable for both fibre telecommunication and silicon photonics. The properties of the ${I}_{15/2}\leftrightarrow{I}_{13/2}$ optical transition in Er:YSO have already been extensively studied. Over two decades ago, improvements in $Er^{3+}$ dephasing time at 1.5 um were achieved by applying a 5T field along the D1 axis. More recently, a record 4.4 ms coherence time on the same optical transition was achieved using a 7T field. These investigations, among others, illustrate that large Er electron spins become thermally polarised with sufficient magnetic field. However, no long lived and coherent spin transitions associated with the Er ions had previously been identified, and such transitions are necessary for on-demand quantum state storage. To address this requirement, the optical and hyperfine transition properties of 167-Er:YSO were investigated in large magnetic fields. In a field of 7T, spectral hole lifetimes of 1 minute and hyperfine population lifetimes of 12 minutes were observed. These measurements illustrate the effect of spin-lattice relaxation in this system, and how it can be mitigated. Efficient spin-polarisation of the entire 167-Er hyperfine ensemble is also demonstrated. This is the first such demonstration in rare earth systems, and a key requirement for broadband optical storage. Moreover, a 1.3 second coherence time was recorded for an 167-Er:YSO hyperfine transition at 7T and 1.4 K. This is an improvement of several orders-of-magnitude over previous coherence measurements on spin-transitions in Er doped solids. This is also sufficient for maximal entanglement rates in quantum repeater networks that span distances of 1000 km or greater. With an optical transition at 1.5 um, Er is also an ideal candidate to connect silicon based quantum computers to the future quantum Internet. In particular, single Er:Si ions could be used to develop an optical-spin bus between P:Si qubits and fibre based quantum networks. Presented here is the first spectroscopic investigation of single Er:Si ions. This required a novel opto-electronic approach to single ion detection, where the Er ions are implanted into a nanometre scale fin-shaped Field Effect Transistor. With this approach it was possible to develop high resolution optical spectra, where both the electronic and hyperfine levels of individual Er ions were resolved. Long optical and spin coherence times are also important requirements for an optical-spin bus. To address the first requirement, an investigation of the optical lineshape was undertaken. Here it was determined that sources of Stark noise external to the transistor channel contribute a significant amount to optical homogeneous linewidth. However, the dominant noise contribution was determined to be short-range (from within the 30 nm wide channel) and the total homogeneous linewidth was measured to be 50 MHz. The site structure of an individual Er:Si ion was then analysed, using magnetic field rotation patterns and optical transitions between multiple crystal field levels. This site was determined to have approximately axial ($C_{3}$) symmetry. The purpose of this study was to determine a magnetic field regime in which the Er electrons spin can be polarised, which is necessary for realising of long hyperfine lifetimes and coherence times.

Jan 1, 20173 citations

Prediction of optical polarization and high-field hyperfine structure via a parametrized crystal-field model for low-symmetry centers in Er3+ -doped Y2SiO5

Nicholas Jobbitt, J.‐P. R. Wells, Michael F. Reid +3 more

We report on the development and application of a parametrized crystal-field model for both ${\mathrm{C}}_{1}$ symmetry centers in trivalent erbium-doped ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ . High-resolution Zeeman and temperature dependent absorption spectroscopy was performed to acquire the necessary experimental data. The obtained data, in addition to the ground $(^{4}\mathrm{I}_{15/2}{\mathrm{Z}}_{1})$ state and exited $(^{4}\mathrm{I}_{13/2}{\mathrm{Y}}_{1})$ state Zeeman and hyperfine structure, were simultaneously fitted in order to refine an existing crystal-field interpretation of the ${\mathrm{Er}}^{3+}$ : ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ system. We demonstrate that it is possible to account for the electronic, magnetic, and hyperfine structure of the full $4{f}^{11}$ configuration of ${\mathrm{Er}}^{3+}$ : ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ and further, that it is possible to predict both optical polarization behavior and high magnetic field hyperfine structure of transitions in the $1.5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ telecommunications band.We report on the development and application of a parametrized crystal-field model for both ${\mathrm{C}}_{1}$ symmetry centers in trivalent erbium-doped ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$. High-resolution Zeeman and temperature dependent absorption spectroscopy was performed to acquire the necessary experimental data. The obtained data, in addition to the ground $(^{4}\mathrm{I}_{15/2}{\mathrm{Z}}_{1})$ state and exited $(^{4}\mathrm{I}_{13/2}{\mathrm{Y}}_{1})$ state Zeeman and hyperfine structure, were simultaneously fitted in order to refine an existing crystal-field interpretation of the ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ system. We demonstrate that it is possible to account for the electronic, magnetic, and hyperfine structure of the full $4{f}^{11}$ configuration of ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ and further, that it is possible to predict both optical polarization behavior and high magnetic field hyperfine structure of transitions in the $1.5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ telecommunications band.

arXiv:2206.09080Physical review. B./Physical review. BOct 13, 202115 citations

Hyperfine interaction of Er 3 + ions in Y 2 Si O 5 : An electron paramagnetic resonance spectroscopy study

O. Guillot-Noël, Philippe Goldner, Y. Le Du +3 more

Electron paramagnetic resonance (EPR) spectroscopy of rare earth ions in crystals is a powerful tool to analyze the hyperfine structure of the rare earth ground state. This can be useful for coherent spectroscopy and quantum information applications where the hyperfine structure of the electronic levels is used. In this work, we give a detailed analysis of the hyperfine structure of the ground state $[^{4}I_{15∕2}(0)]$ of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ . The electronic Zeeman, hyperfine, and quadrupole matrices are obtained from angular variations of the magnetic field in three orthogonal crystal planes. An excellent agreement is obtained between experimental and simulated magnetic field positions and relative intensities of EPR lines.Electron paramagnetic resonance (EPR) spectroscopy of rare earth ions in crystals is a powerful tool to analyze the hyperfine structure of the rare earth ground state. This can be useful for coherent spectroscopy and quantum information applications where the hyperfine structure of the electronic levels is used. In this work, we give a detailed analysis of the hyperfine structure of the ground state $[^{4}I_{15∕2}(0)]$ of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$. The electronic Zeeman, hyperfine, and quadrupole matrices are obtained from angular variations of the magnetic field in three orthogonal crystal planes. An excellent agreement is obtained between experimental and simulated magnetic field positions and relative intensities of EPR lines.

Physical Review BDec 11, 200681 citations

High-resolution magneto-optical spectroscopy of LiYF47:Er3+167,Er3+166 and analysis of hyperfine structure of ultranarrow optical transitions

K. I. Gerasimov, Mansur M. Minnegaliev, Malkin Boris Zalmanovich +2 more

We performed high-resolution magneto-optical spectroscopy of the hyperfine transitions from $^{4}I_{15/2}$ to the $^{4}I_{13/2}$ and $^{4}I_{9/2}$ multiplets of $^{167}\mathrm{Er}^{3+}$ and $^{166}\mathrm{Er}^{3+}$ in an isotopically purified $^{7}\mathrm{LiYF}_{4}$ crystal in various external magnetic fields up to 0.7 T. The obtained experimental results are interpreted in the framework of the generalized theoretical approach. The derived model successfully explains all the experimentally observed optical hyperfine transitions by using a single set of basic parameters found for the crystal-field interaction, magnetic dipole and electric quadrupole hyperfine interactions, together with Zeeman interactions at different orientations of the external magnetic field. A number of the studied quantum transitions appears to be promising for use in Raman quantum storage at optical telecommunication wavelengths.We performed high-resolution magneto-optical spectroscopy of the hyperfine transitions from $^{4}I_{15/2}$ to the $^{4}I_{13/2}$ and $^{4}I_{9/2}$ multiplets of $^{167}\mathrm{Er}^{3+}$ and $^{166}\mathrm{Er}^{3+}$ in an isotopically purified $^{7}\mathrm{LiYF}_{4}$ crystal in various external magnetic fields up to 0.7 T. The obtained experimental results are interpreted in the framework of the generalized theoretical approach. The derived model successfully explains all the experimentally observed optical hyperfine transitions by using a single set of basic parameters found for the crystal-field interaction, magnetic dipole and electric quadrupole hyperfine interactions, together with Zeeman interactions at different orientations of the external magnetic field. A number of the studied quantum transitions appears to be promising for use in Raman quantum storage at optical telecommunication wavelengths.

Physical review. B./Physical review. BAug 29, 201629 citations

Magnetic g tensors for the I 15 ∕ 2 4 and I 13 ∕ 2 4 states of Er 3 + : Y 2 Si O 5

Yongchen Sun, Thomas Böttger, Charles W. Thiel +1 more

We present the complete Zeeman $g$ tensors for the lowest-energy $^{4}\mathrm{I}_{15∕2}$ and $^{4}\mathrm{I}_{13∕2}$ states of ${\mathrm{Er}}^{3+}$ doped into ${\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ for both crystallographic sites deduced from orientation-dependent optical Zeeman spectroscopy over three orthogonal crystal planes. From these data, principal axes of the $g$ tensors were determined for each crystallographic site. Along axes with maximum values, the effective $g$ factors are 14.65 (site 1) and 15.46 (site 2) for the ground state, and 12.97 (site 1) and 13.77 (site 2) for the excited state. To minimize optical decoherence and spectral diffusion in device applications and high resolution spectroscopy, special directions for applying an external magnetic field have been found for each site, for which the ground- and excited-state $g$ factors are equal. Among those directions, choices are presented that also maximize the ground-state splittings for all four magnetically inequivalent sites, thus optimizing the prospects for freezing out electron spin fluctuations and reducing decoherence and spectral diffusion significantly.We present the complete Zeeman $g$ tensors for the lowest-energy $^{4}\mathrm{I}_{15∕2}$ and $^{4}\mathrm{I}_{13∕2}$ states of ${\mathrm{Er}}^{3+}$ doped into ${\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ for both crystallographic sites deduced from orientation-dependent optical Zeeman spectroscopy over three orthogonal crystal planes. From these data, principal axes of the $g$ tensors were determined for each crystallographic site. Along axes with maximum values, the effective $g$ factors are 14.65 (site 1) and 15.46 (site 2) for the ground state, and 12.97 (site 1) and 13.77 (site 2) for the excited state. To minimize optical decoherence and spectral diffusion in device applications and high resolution spectroscopy, special directions for applying an external magnetic field have been found for each site, for which the ground- and excited-state $g$ factors are equal. Among those directions, choices are presented that also maximize the ground-state splittings for all four magnetically inequivalent sites, thus optimizing the prospects for freezing out electron spin fluctuations and reducing decoherence and spectral diffusion significantly.

Physical Review BFeb 29, 200891 citations

^{4}\mathrm{I}_{15/2}

ground and

^{4}\mathrm{I}_{13/2}

{I}_{15/2}\leftrightarrow{I}_{13/2}

optical transition in Er:YSO have already been extensively studied. Over two decades ago, improvements in

Er^{3+}

dephasing time at 1.5 um were achieved by applying a 5T field along the D1 axis. More recently, a record 4.4 ms coherence time on the same optical transition was achieved using a 7T field. These investigations, among others, illustrate that large Er electron spins become thermally polarised with sufficient magnetic field. However, no long lived and coherent spin transitions associated with the Er ions had previously been identified, and such transitions are necessary for on-demand quantum state storage. To address this requirement, the optical and hyperfine transition properties of 167-Er:YSO were investigated in large magnetic fields. In a field of 7T, spectral hole lifetimes of 1 minute and hyperfine population lifetimes of 12 minutes were observed. These measurements illustrate the effect of spin-lattice relaxation in this system, and how it can be mitigated. Efficient spin-polarisation of the entire 167-Er hyperfine ensemble is also demonstrated. This is the first such demonstration in rare earth systems, and a key requirement for broadband optical storage. Moreover, a 1.3 second coherence time was recorded for an 167-Er:YSO hyperfine transition at 7T and 1.4 K. This is an improvement of several orders-of-magnitude over previous coherence measurements on spin-transitions in Er doped solids. This is also sufficient for maximal entanglement rates in quantum repeater networks that span distances of 1000 km or greater. With an optical transition at 1.5 um, Er is also an ideal candidate to connect silicon based quantum computers to the future quantum Internet. In particular, single Er:Si ions could be used to develop an optical-spin bus between P:Si qubits and fibre based quantum networks. Presented here is the first spectroscopic investigation of single Er:Si ions. This required a novel opto-electronic approach to single ion detection, where the Er ions are implanted into a nanometre scale fin-shaped Field Effect Transistor. With this approach it was possible to develop high resolution optical spectra, where both the electronic and hyperfine levels of individual Er ions were resolved. Long optical and spin coherence times are also important requirements for an optical-spin bus. To address the first requirement, an investigation of the optical lineshape was undertaken. Here it was determined that sources of Stark noise external to the transistor channel contribute a significant amount to optical homogeneous linewidth. However, the dominant noise contribution was determined to be short-range (from within the 30 nm wide channel) and the total homogeneous linewidth was measured to be 50 MHz. The site structure of an individual Er:Si ion was then analysed, using magnetic field rotation patterns and optical transitions between multiple crystal field levels. This site was determined to have approximately axial (

C_{3}

) symmetry. The purpose of this study was to determine a magnetic field regime in which the Er electrons spin can be polarised, which is necessary for realising of long hyperfine lifetimes and coherence times.

We report on the development and application of a parametrized crystal-field model for both

{\mathrm{C}}_{1}

symmetry centers in trivalent erbium-doped

{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}

. High-resolution Zeeman and temperature dependent absorption spectroscopy was performed to acquire the necessary experimental data. The obtained data, in addition to the ground

(^{4}\mathrm{I}_{15/2}{\mathrm{Z}}_{1})

state and exited

(^{4}\mathrm{I}_{13/2}{\mathrm{Y}}_{1})

state Zeeman and hyperfine structure, were simultaneously fitted in order to refine an existing crystal-field interpretation of the

{\mathrm{Er}}^{3+}

{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}

system. We demonstrate that it is possible to account for the electronic, magnetic, and hyperfine structure of the full

4{f}^{11}

configuration of

{\mathrm{Er}}^{3+}

{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}

and further, that it is possible to predict both optical polarization behavior and high magnetic field hyperfine structure of transitions in the $1.5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ telecommunications band.

[^{4}I_{15∕2}(0)]

{\mathrm{Er}}^{3+}

ions in

{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}

. The electronic Zeeman, hyperfine, and quadrupole matrices are obtained from angular variations of the magnetic field in three orthogonal crystal planes. An excellent agreement is obtained between experimental and simulated magnetic field positions and relative intensities of EPR lines.

We performed high-resolution magneto-optical spectroscopy of the hyperfine transitions from

^{4}I_{15/2}

to the

^{4}I_{13/2}

and

^{4}I_{9/2}

multiplets of

^{167}\mathrm{Er}^{3+}

and

^{166}\mathrm{Er}^{3+}

in an isotopically purified

^{7}\mathrm{LiYF}_{4}

crystal in various external magnetic fields up to 0.7 T. The obtained experimental results are interpreted in the framework of the generalized theoretical approach. The derived model successfully explains all the experimentally observed optical hyperfine transitions by using a single set of basic parameters found for the crystal-field interaction, magnetic dipole and electric quadrupole hyperfine interactions, together with Zeeman interactions at different orientations of the external magnetic field. A number of the studied quantum transitions appears to be promising for use in Raman quantum storage at optical telecommunication wavelengths.

We present the complete Zeeman

g

tensors for the lowest-energy

^{4}\mathrm{I}_{15∕2}

and

^{4}\mathrm{I}_{13∕2}

states of

{\mathrm{Er}}^{3+}

doped into

{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}

for both crystallographic sites deduced from orientation-dependent optical Zeeman spectroscopy over three orthogonal crystal planes. From these data, principal axes of the

g

tensors were determined for each crystallographic site. Along axes with maximum values, the effective

g

factors are 14.65 (site 1) and 15.46 (site 2) for the ground state, and 12.97 (site 1) and 13.77 (site 2) for the excited state. To minimize optical decoherence and spectral diffusion in device applications and high resolution spectroscopy, special directions for applying an external magnetic field have been found for each site, for which the ground- and excited-state

g

factors are equal. Among those directions, choices are presented that also maximize the ground-state splittings for all four magnetically inequivalent sites, thus optimizing the prospects for freezing out electron spin fluctuations and reducing decoherence and spectral diffusion significantly.